(105f) A Distributed Feedback Optimizing Control Framework for Large-Scale Coupled Systems with Convergence Guarantees

Distributed real-time optimization (RTO) enables optimal operation of large-scale coupled process systems with common resources shared across several clusters. Typically, in distributed RTO, the different subsystems are optimized locally, and a centralized master problem is used to coordinate the different subsystems in order to reach system-wide optimal operation. This is especially beneficial in eco-industrial parks with shared common resources, where only limited information can be shared between the different subsystems.

However, the use of distributed RTO methods in practice remains rather low [1]. The main reasons for this are attributed to the computational cost of solving the numerical optimization problems online, and the slow convergence rate. Currently, there is active research to improve the rate of convergence, such that the master and subproblems converge to a feasible optimal solution in a small number of iterations/communication rounds (see [1] and the references therein). Despite the algorithmic developments to improve the convergence rate, the subproblems still need to solve numerical optimization problems online at each iteration, which is often the main computational bottleneck in real-time optimization.

Feedback optimizing control, also commonly known as direct input adaptation, is a class of RTO methods that circumvents the need to solve computationally intensive optimization problems. The concept of feedback optimizing control dates back to the 1980s [2], where steady-state optimal process operation is achieved by directly manipulating the input using feedback control [2,3]. However, feedback optimizing control, in general, is more suited for unit operations, or for small-scale processes. In large-scale systems, this leads to a decentralized control structure, where some clusters of operating units are optimized locally without any coordination. When the system is coupled in one form or the other, system-wide optimal operation does not result from the aggregates of individual operating units in a decentralized fashion [2].

In order to address this issue, we present a distributed feedback optimizing control framework, where the local subproblems are converted into control problems that are coordinated by a master problem. Particularly, in this talk

- we first present a generic framework where the augmented Lagrangian of the optimization problem is used to express the “optimizing” controlled variables (CV) for each subproblem as a function of the Lagrange multipliers. When controlled to a constant setpoint locally, this leads to optimal operation of the local subsystem, and as the master coordinator updates the Lagrange multipliers, this leads to system-wide optimal operation [4].

- we show that by using the augmented Lagrange function, the proposed distributed feedback optimizing control framework converges to a KKT point of the overall optimization problem under mild assumptions [4].

- we then demonstrate the performance of the proposed approach using an optimal resource allocation problem in an industrial symbiotic oil production network [4].

To this end, the proposed approach enables industrial symbiosis without the need to solve numerical optimization problems online. In addition, it also broadens the applicability of feedback optimizing control to large-scale systems with complex interconnections. The proposed framework can also be used with any model-based or model-free feedback optimizing control approach, or a combination of both, making it broadly applicable. Another advantage of the proposed approach is that it enables the different local controllers to be implemented at different sampling rates, which is often desirable in a heterogenous network of systems.

References

[1] Wenzel, S., Riedl, F. and Engell, S., 2020. An efficient hierarchical market-like coordination algorithm for coupled production systems based on quadratic approximation. Computers & Chemical Engineering, 134, p.106704.

[2] Morari, M., Arkun, Y. and Stephanopoulos, G., 1980. Studies in the synthesis of control structures for chemical processes: Part I: Formulation of the problem. Process decomposition and the classification of the control tasks. Analysis of the optimizing control structures. AIChE Journal, 26(2), pp.220-232.

[3] Chachuat, B., Srinivasan, B. and Bonvin, D., 2009. Adaptation strategies for real-time optimization. Computers & Chemical Engineering, 33(10), pp.1557-1567.

[4] Krishnamoorthy, D., 2021. A distributed feedback-based online process optimization framework for optimal resource sharing. Journal of Process Control, 97, pp.72-83.